20 citations · 67 across the 16 of their papers we have counts for
20 papers
Szemerédi's Theorem Along Cantor Sets of Integers
Alex Burgin, Anastasios Fragkos, Michael T. Lacey +2
Let be Cantor set of integers, that is a set of integers with restricted digits modulo a base , and suppose is one of the restricted digit…
Integer Cantor Sets: Arithmetic Combinatorial Properties
Alex Burgin, Anastasios Fragkos, Michael T. Lacey +2
Cantor sets of integers have a rich set of arithmetic combinatorial properties. We consider classical Cantor sets, with a base and a fixed set of allowed digits. For such sets, we…
Weighted Weak Type estimates for non-integral Square Functions
Dario Mena, Maria Carmen Reguera, Luz Roncal
We provide quantitative weighted weak type estimates for non-integral square functions in the critical case in terms of the and reverse Hölder constants associated to t…
Quadratic sparse domination and Weighted Estimates for non-integral Square Functions
Julian Bailey, Gianmarco Brocchi, Maria Carmen Reguera
We prove a quadratic sparse domination result for general non-integral square functions . That is, we prove an estimate of the form \begin{equation*} \int_{M} (S f)^{2} g \, \ma…
Unboundedness of potential dependent Riesz transforms for totally irregular measures
Julian Bailey, Andrew J. Morris, Maria Carmen Reguera
We prove that, for totally irregular measures on with , the -dimensional Riesz transform $$ T_{A,μ}^{V}f(x) = \int_{\mathbb{R}^d} \nabla_{1}\mat…
A matrix weighted bilinear Carleson Lemma and Maximal Function
Stefanie Petermichl, Sandra Pott, Maria Carmen Reguera
We prove a bilinear Carleson embedding theorem with matrix weight and scalar measure. In the scalar case, this becomes exactly the well known weighted bilinear Carleson embedding t…